Chamfering is done to revolver cylinders (i.e., the actual hole where each cartridge is inserted), at the back where the case rim sits. It is beveling of the sharp 90-degree angle.
The purpose is to facilitate insertion of cartridges into the cylinders. Some sharp-shouldered and hollowpoint ammo sometimes hangs up on the front edge of the cylinder, especially when using a speedloader. Chamfering breaks the edge and makes it easier to "funnel" the bullet noses into the chambers.
Brownell's sells a chamfering tool that works well. It is not too hard to use for one who is competant with hand tools.